1st thing I would check is.. tire pressure make sure they are good with specs..
since thats free

next check your tires.. make sure they are good.. are they balanced ? make sure you check entire tire.. when I say that I mean also the sidewalls towards the engine side.. not just the outter..

next would be your brakes and rotors.. if your rotors are not even or smooth.. when you step on the brake you willl get a shaky steering wheel... which happened in my case..

because I did not replace rotors when replacing brakes the first time.. so second time around I replaced both rotors and brakes and steering vibration was gone... I usually get shaky steering when I step on the brake and higher speeds.

check that.. next would be your control arms ? and other suspension issues.. but I think if you checked the above you should be good to go.